Stability of nonlinear stochastic systems under event-triggered impulsive control with distributed-delay impulses.

This paper investigated the stability of nonlinear stochastic systems with distributed-delay impulses within the framework of event-triggered impulsive control (ETIC). A continuous event-triggered mechanism (ETM) with a fixed waiting time and a periodic ETM with a fixed sampling period were proposed, effectively eliminating the occurrence of Zeno behavior. By employing the Lyapunov method and mathematical induction, a set of sufficient conditions was established to ensure the p-th moment uniform stability (p-US) and p-th moment exponential stability (p-ES) of the considered system. Furthermore, the theoretical results were applied to a class of nonlinear stochastic systems. Utilizing the linear matrix inequality (LMI) approach, a joint design of the ETM and impulsive control gains was achieved. Finally, numerical examples were provided to demonstrate the effectiveness and feasibility of the proposed theoretical results.